Simplifying 5-point tensor reduction

The 5-point tensors have the property that after insertion of the metric tensor g in terms of external momenta, all g -contributions in the tensor decomposition cancel.If furthermore the tensors are contracted with external momenta, the inverse 5-point Gram determinant () 5 cancels automatically.If the remaining 4-point sub-Gram determinant s s 5 is not small then this approach appears to be particularly efficient in numerical calculations.We also indicate how to deal with small s s 5 .Explicit formulae for tensors of degree 2 and 3 are given for large and small (sub-) Gram determinants.